No one has ever been sure what to do with Edward Burra, the British painter whose most celebrated work was produced in the 1920s and 30s. Looked at one way, he's a satirist along the lines of Otto Dix or George Grosz, a social realist with a sharp distorting eye for the human figure writhing and bridling its way through various vanity fairs. Looked at another way, though, Burra is a romantic landscapist, with all the yearning for English soil of his friend and sometime mentor Paul Nash. But then there are the bright colours, the oranges, blues and greens that flash out from his work, which hardly fit with modernism's subfusc palette and pared-down aesthetic. It is all very confusing, which is why some art historians have dismissed Burra as an aberration.

They won't be able to get away with that for much longer. A new exhibition at the Pallant House Gallery, Chichester, of 70 of Burra's most important paintings is proof, if any were still needed, that he is simply too good to be sidelined. And the art market clearly thinks so too. At a Sotheby's auction earlier this year, Zoot Suits, Burra's depiction of dapperly dressed West Indian men in post-war Notting Hill, went for a record-breaking £2m.

To understand the reasons for Burra's critical marginalisation you have to go back to his biography. A lifelong struggle with rheumatoid arthritis and a debilitating blood disease meant that he was never able to use an easel in the conventional way. Instead he opted to sit, working mostly in unfashionable watercolour on thick paper laid flat on a table. His chronic ill health also prevented him from being a joiner of artistic groups and cliques. Although nominally a Surrealist and briefly a member of Paul Nash's Unit One group during the 30s, for the most part Burra went his own sweet way.

There was, though, nothing remotely parochial about the work. As one of the main rooms in the Pallant House exhibition reveals, Burra delighted in travel and it is his blazingly coloured studies of streetlife in Paris, Marseilles and Harlem of the interwar period that are most instantly recognisable today. In Market Day (1926), two recently disembarked black sailors saunter along a chaotic dockside. Merchant ships unload, couples court and prostitutes jut their hips hopefully forward. A wealth of detail plays across the picture's surface, ranging from the jazzy necktie worn by one of the sailors, to the bowl of fruit balanced on the head of a female passerby, like some demotic Carmen Miranda. Phallic jokes abound, with obscene shapes thrusting up and out from every corner. This, though, is no invitation to a debauch. The viewer – like the artist – remains above the fray, surveying the scene from a steadier place.

Burra's biographer, Jane Stevenson, suggests that the most helpful way to think of him is as a "camera", much like that contemporary fellow-flâneur Christopher Isherwood. Burra's pictures, though, were not made on the spot: blessed with a photographic memory, he reworked images of Harlem, Paris and Marseilles in the calm of rural Sussex, where he continued to live with his parents in the house in which he was born. It was here, with the addition of nothing more complicated than a dollop of spit, that he was able to make his watercolour glow as rich and dense as any oil. At the same time, the fluidity of the medium allowed Burra to produce a velvet-smooth finish, all the more remarkable given the way he was obliged to jam the brush into his arthritic hand. George Melly, a fellow Surrealist and close friend, would continue to wonder out loud at the way that Burra's fused paw became "an unlikely instrument of so much precise beauty".

Although put down for Eton at birth, Burra's health meant that he was home-schooled from the age of 12. The happy result was that he received an education that ranged wider than that of most boys of his class, including a deep immersion in French literature. At the age of 16 he was allowed to enroll at Chelsea College of Art, from where he proceeded to the RCA. It was there that he established the friendships that would support him all his life: with photographer Barbara Ker-Seymer, the costume designer "Bumble" Dawson and, closest of all, Billy Chappell, a ballet dancer through whom Burra was introduced to the world of avant-garde dance. (The exhibition includes some visual references to the ground-breaking sets and costumes that Burra designed for Frederick Ashton and Ninette de Valois, including a stunning front cloth for Don Quixote from 1950.) While in no sense a misanthrope, Burra protected his privacy. The story goes that one day, he told his mother he was going into the garden and disappeared to America for six months. Even towards the end of his life he was proudly announcing, in that strange drawl affected by bright young people in the 20s: "I never tell anybody anything."

In other ways, though, Burra's boundaries were porous and his heart wide open. Many of his street scenes, including Market Day, are noticeably crammed with faces of every colour. Black culture had fascinated Burra from his teenage years when he had first come to love imported American jazz. Trips to Paris from the mid-20s gave him the chance to sit entranced at the Revue Nègre where Josephine Baker shimmied through her sensational dance routines. Later, in the mid-30s, Burra landed in Harlem at the height of its cultural Renaissance. It was at this time that he produced some of his most instantly identifiable work, including a series of scenes in which various pairs of snappily-dressed dudes conduct deals of doubtful legality while ambiguous figures prowl the frame. His Savoy Ballroom (1934) pulses with the beat of cool jazz as couples dance themselves into delightful oblivion.

Burra combined this sharp eye for contemporary urban life with a deep knowledge and affection for the art of the past. Around the time he first started painting in the 20s, there was a revival of interest in "the conversation piece", an 18th-century genre in which a group of genteel friends or relatives are painted decorously talking, playing cards or taking tea. With a sly wit harnessed to impeccable technique, Burra inverted convention and made the conversation a downright dirty thing. In The Two Sisters (1929), he shows a pair of identical women drinking coffee while plushly seated in a neo-classical courtyard. Disreputable detail, though, soon starts to press forward. The two sisters are embalmed with rouge and lipstick while their dresses fall open to show breasts and nipples. The maid serving drinks is revealed, on closer look, to be a beefy man in drag.

Burra's aesthetic, then, was always camp and often explicitly gay. In Dockside Café, Marseilles (1929), the two women entwined behind the bar are clearly male transvestites, while the sailor-customer wears a bright pink jumper matched with ballet shoes complete with criss-cross ribbons. (Burra being Burra there is also a phallic coffee pot handle jutting from the sailor's crotch at an opportune angle.) It would be misleading, though, to read his life directly from his art. While it is true that he was always drawn to places where transgressive sexualities flourished – clubs, cafés, anonymous street corners – he himself remained, camera-like, a non-participating observer. The thousands of letters Burra wrote to his close friends, now archived at the Tate, may bounce along in high camp style – men are routinely referred to as "she", and everyone is "dearie" – but it remains essentially a textual performance. Burra was happy to label himself a sexless creature. The only time he admitted to an erection – a weak one at that – was while watching a film of Mae West.

The counterweight to all this filthy talk was, incongruously, daily life in Rye, East Sussex, 30 or so miles up the coast from Chichester. Burra's Rye was also the Rye of EF Benson's Mapp and Lucia novels, a picture-postcard town bubbling with small-town social and cultural anxieties. The wealthy Burras were happily above all that. Their handsome mansion was surrounded by 11 buffering acres and they were too secure to worry about what the neighbours thought. Nonetheless Burra knew enough of what he called "Tinkerbelle Towne" and its twitchy inhabitants to want to poke fun. In The Tea Shop (1929), the mimsy local patrons are served by nubile waitresses, who are naked apart from a raffish hat or tiny pinny. There are the usual visual puns on show: the coffee poured by one waitress seems to fall on the cloche hat of a lady customer, pop-eyed with shock, while another's thrown-back heel appears to be kicking the naked bottom of the waitress immediately behind. The inhabitants of Benson's Rye might have liked to flatter themselves that they were "up" on contemporary art, but this, you suspect, would have been enough to send them skittering over the edge.

Although Burra will probably always remain best known for his early images of city life, his painting continued to develop throughout his career. As the 30s darkened, he followed the example of his beloved Goya and painted the cruelty of war, especially the tragedy of turning innocent young men into killing machines. By the 50s, in a shift that disappointed some of his admirers, Burra turned to making lyrical accounts of the British countryside. Look carefully, though, and you will see that there is nothing easy or consoling about the images he produced in middle age. In the bucolic-sounding The Cabbage Harvest (1943-45) a lowering sky hangs over a menacing foreground in which sacks of cabbages are piled like rocks and feebly tugged by two febrile-looking men. The setting of this and other landscape paintings may be Sussex, but it is a Sussex of rusting farm machinery, animal skulls and the unnerving sense that everyone would rather be somewhere else. Later, in the 60s and 70s, Burra commented more directly on the unravelling of the English countryside taking place around him. He produced a series of powerful paintings in which diggers, lorries and tractors morph into monsters ripping through the landscape with a hungry, polluting lust.

By the time he produced these works, Burra's own horizons had shrunk. Following the death of his mother in the 1960s, he moved into a small cottage in the grounds of the family home. His sister came in every day and there were occasional motoring holidays around Britain with Billy Chappell, during which Burra would periodically stiffen, and fix an image on his all-seeing eye. He continued to be obsessed with his work to the exclusion of all else, explaining in a rare moment of candour that the only time he was not in pain was when he was painting. In a filmed interview given towards the end of his life, Burra declared, or rather drawled, "I think you ought to work, to paint. Otherwise, if you don't do enough painting, what's the point of it all?" He died in 1976 at the age of 72 having lived far longer – and triumphantly – than anyone could possibly have predicted.